The problem is to prove that $\displaystyle \frac{dy}{dx}=\frac{-1}{(x+1)^2} $when $\displaystyle x\sqrt{y+1}+y\sqrt{x+1}=0$. I tried substituting $\displaystyle x=\tan^2\theta$ and $\displaystyle y=\tan^2\phi$ but then I got stuck. I tried many other things but this was the only notable one.

thanks.